LiL-Q applies quasilinearization to nonlinear PDEs and solves each resulting linear problem by convex least-squares collocation on Linear-in-Learnables trial spaces, achieving fast convergence and high accuracy on multiple benchmarks.
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When and why pinns fail to train: A neural tangent kernel perspective
15 Pith papers cite this work, alongside 1,177 external citations. Polarity classification is still indexing.
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An adaptive KAN-based PINN framework for axisymmetric pulsar magnetosphere achieves O(1e-6) PDE residual errors, under-20-minute convergence, smaller stellar radii, and a correction to the flux-T-point equation.
The curvature-aware precision controller adapts between FP32 and FP64 during PINN training to match double-precision accuracy at reduced computational cost.
A per-instance learned graph-network transfer between coarse and fine discrete-field optimizations improves Darcy and EIT coefficient reconstructions without surrogates or pretraining.
A coupled LSTM-GNN model reconstructs local elasto-plastic stress fields from macroscopic loading paths on a plate-with-hole microstructure, achieving 1000x speedup and mesh transferability with 1.9% error.
PINN-AFE uses multi-head attention and input convex networks to solve Monge-Ampère equations with claimed accuracy, efficiency, and extensions to image enhancement and medical registration.
P-GONE applies generative ML to optimize Trotter-Suzuki decompositions, reporting up to 19.4x circuit depth reduction at F >= 0.95 versus Qiskit baselines on structured Hamiltonians.
An adaptive anisotropic composite quadrature strategy combined with refresh-based training narrows the gap between training and reference losses in neural residual minimization for PDEs while using quadrature points more efficiently.
Bio-PINNs with a near-to-far curriculum and deformation-uncertainty proxy recover cell-induced densified phases and tether morphologies more reliably than standard adaptive PINN baselines in single-cell and multicellular settings.
ActNet is a new KST-based neural network that outperforms KANs and competes with MLPs in PINN benchmarks for PDE simulation tasks.
INI-VPINN is a new weak-form PINN formulation that implicitly enforces Neumann and interface conditions for Poisson and Laplace problems in multi-material domains with geometric singularities.
RBF-RLS outperforms PINNs on PDEs with Dirac deltas via weak-form integration, delivering consistent forward and inverse solutions for linear transport problems in porous media and rivers.
A heteroscedastic uncertainty PINN with warm-start and deep ensembles for SAR flood inference claims 25% IoU gain by relaxing physics constraints in high-noise regions.
StableGrad applies scale correction to weight gradients after backpropagation to enable stable optimization of deep BatchNorm-free networks including PINNs.
An attention-based physics-guided CNN surrogate is trained to predict long-time microstructural evolution under the Cahn-Hilliard equation for both critical and off-critical mixtures while preserving composition and matching Lifshitz-Slyozov domain growth.
citing papers explorer
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A Convex Quasilinearization Method for Solving Nonlinear PDEs with Physics-Informed Neural Networks
LiL-Q applies quasilinearization to nonlinear PDEs and solves each resulting linear problem by convex least-squares collocation on Linear-in-Learnables trial spaces, achieving fast convergence and high accuracy on multiple benchmarks.
-
An adaptive framework for the axisymmetric pulsar magnetosphere using physics-informed Kolmogorov-Arnold networks
An adaptive KAN-based PINN framework for axisymmetric pulsar magnetosphere achieves O(1e-6) PDE residual errors, under-20-minute convergence, smaller stellar radii, and a correction to the flux-T-point equation.
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Curvature-aware dynamic precision approach for physics-informed neural networks
The curvature-aware precision controller adapts between FP32 and FP64 during PINN training to match double-precision accuracy at reduced computational cost.
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ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems
A per-instance learned graph-network transfer between coarse and fine discrete-field optimizations improves Darcy and EIT coefficient reconstructions without surrogates or pretraining.
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Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks
A coupled LSTM-GNN model reconstructs local elasto-plastic stress fields from macroscopic loading paths on a plate-with-hole microstructure, achieving 1000x speedup and mesh transferability with 1.9% error.
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Physics-Informed Neural Networks with Attention Feature Expansion for Monge-Amp\`ere Equations
PINN-AFE uses multi-head attention and input convex networks to solve Monge-Ampère equations with claimed accuracy, efficiency, and extensions to image enhancement and medical registration.
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Physics Guided Generative Optimization for Trotter Suzuki Decomposition
P-GONE applies generative ML to optimize Trotter-Suzuki decompositions, reporting up to 19.4x circuit depth reduction at F >= 0.95 versus Qiskit baselines on structured Hamiltonians.
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Adaptive anisotropic composite quadratures for residual minimisation in neural PDE approximations
An adaptive anisotropic composite quadrature strategy combined with refresh-based training narrows the gap between training and reference losses in neural residual minimization for PDEs while using quadrature points more efficiently.
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Cell-induced densification and tether formation in fibrous extracellular matrices with biomimetic physics-informed neural networks
Bio-PINNs with a near-to-far curriculum and deformation-uncertainty proxy recover cell-induced densified phases and tether morphologies more reliably than standard adaptive PINN baselines in single-cell and multicellular settings.
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Deep Learning Alternatives of the Kolmogorov Superposition Theorem
ActNet is a new KST-based neural network that outperforms KANs and competes with MLPs in PINN benchmarks for PDE simulation tasks.
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INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities
INI-VPINN is a new weak-form PINN formulation that implicitly enforces Neumann and interface conditions for Poisson and Laplace problems in multi-material domains with geometric singularities.
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Physics-Informed Neural Networks and Radial Basis Functions for PDEs with Dirac Delta Sources
RBF-RLS outperforms PINNs on PDEs with Dirac deltas via weak-form integration, delivering consistent forward and inverse solutions for linear transport problems in porous media and rivers.
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Overcoming "Physics Shock" in Earth Observation A Heteroscedastic Uncertainty Framework for PINN-based Flood Inference
A heteroscedastic uncertainty PINN with warm-start and deep ensembles for SAR flood inference claims 25% IoU gain by relaxing physics constraints in high-noise regions.
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StableGrad: Backward Scale Control without Batch Normalization
StableGrad applies scale correction to weight gradients after backpropagation to enable stable optimization of deep BatchNorm-free networks including PINNs.
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Physics-guided Convolutional Neural Network for Domain Growth Prediction in Systems with Conserved Kinetics
An attention-based physics-guided CNN surrogate is trained to predict long-time microstructural evolution under the Cahn-Hilliard equation for both critical and off-critical mixtures while preserving composition and matching Lifshitz-Slyozov domain growth.